Problem: Simplify the following expression: $n = \dfrac{-10t^3}{-90t^3 - 40t^2}$ You can assume $t \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10t^3 = - (2\cdot5 \cdot t \cdot t \cdot t)$ The denominator can be factored: $-90t^3 - 40t^2 = - (2\cdot3\cdot3\cdot5 \cdot t \cdot t \cdot t) - (2\cdot2\cdot2\cdot5 \cdot t \cdot t)$ The greatest common factor of all the terms is $10t^2$ Factoring out $10t^2$ gives us: $n = \dfrac{(10t^2)(-t)}{(10t^2)(-9t - 4)}$ Dividing both the numerator and denominator by $10t^2$ gives: $n = \dfrac{-t}{-9t - 4}$